where the denominator \(\mathbf {x}_{t+1} - \mathbf {x}_t\)  denotes the 3D scene flow and the the numerator \(\mathbf {o}_{t+1}- \mathbf {o}_t\)  denotes the 3D camera motion, both over one time step forward.
The 3D scene flow can be estimated via the 2D dense optical flow field and the metric depth map when available, or monocular depth map from off-the-shelf approaches [1]}, [2]} in the general case.
Please see the Appendix for more details. Note that \(\Omega \)  in theory captures the effective multi-view factor for any sequence.
However, in practice, 3D scene flow estimation is an actively studied problem and may suffer from noisy or costly predictions.
